There are many situations where it is necessary to determine whether a leak exists in a gas filled container of fixed volume. One example of such a situation is a manufacturing operation where it is necessary to determine and control the concentration of combustible gases in a vessel. A leak makes it difficult for a manufacturer to maintain optimum concentrations of the gas for combustion and other chemical reactions where such gases may be used. A leak of combustible gases, most of which are toxic, also presents a safety hazard to operating personnel who may inhale the vapors or be subject to an explosion. Therefore, it is very important that a reliable method of detecting such leaks be found. The chosen method should provide one with an accurate representation of the magnitude of the leak so that suitable alarms or warnings can be given or so that the quantity of gas remaining in the vessel--usually expressed as the number of moles--may be ascertained. As is well known, a mole equals 6.times.10.sup.23 molecules of any substance.
The prior art is replete with a number of gas analyzers which all serve to monitor the concentration of gases. These devices can, of course, be used to determine whether or not a vessel containing a gas is experiencing a leak because they indicate the number of moles of gas that are contained in the vessel at any time. If the reading given by the device indicates a lower concentration of gas than is expected at any particular time, a leak must exist.
A very common gas analyzer device employs a self-heated hot wire detector which is usually made of platinum. When the combustible gas to be measured contains oxygen, the mixture is fed to the hot wire detector where combustion occurs; the wire serving as a combustion catalyst. A temperature sensor, such as a thermocouple, then measures the temperature rise resulting from the combustion and this measurement is directly related to the concentration of the gas. More frequently, the electrical resistance of the hot wire itself is measured as the means for detecting temperature rise, much as occurs in a typical electrical resistance thermometer. When the sample to be measured does not contain oxygen, air or oxygen must be added to the sample in carefully controlled quantities, but well in excess of combustion requirements, so that the reaction occurring within the detector will be limited only by the amount of combustible gases or vapors present. Wheatstone bridge circuitry is generally used in these instruments, in which case a reference detector is also required.
In another type of gas analyzer, the sample gas is burned in a small pilot flame where the temperature is monitored by a thermocouple. The presence of combustibles in the supply of gas to the pilot causes the flame temperature to increase proportionately with concentration. There are also gas analyzers of the thermal conductivity type which operate on the principle that different gases vary considerably in their ability to conduct heat. Such devices use hot wire gas analyzer cells, a typical cell being comprised of an electrically conductive elongated sensing element that is mounted coaxially inside a cylindrical chamber which contains the gas to be measured. By passage of an electrical current through the element, the cell is maintained at a temperature considerably higher than the cell wall. The equilibrium temperature is reached when all thermal losses from the element have stabilized. The difference of temperature between the element and the cell walls, as displayed by the temperature rise of the element at equilibrium, is a function of the electric power input and the combined rate of heat loss from the wire by gaseous conduction, convection, radiation and conduction through the solid parts of the element. Proper cell design and geometry makes it possible to maximize the heat loss due to gaseous conduction. Thus, a rise in the temperature of the element at constant electric power input is inversely related to the thermal conductivity of the gas within the cell. Normally, a Wheatstone bridge is used to measure resistance change of the sensing element.
As can be seen, these prior-art devices for monitoring the concentration of gases in a vessel are generally cumbersome and difficult to monitor and use. A major improvement over those prior-art devices is a gas leak detector apparatus which is disclosed in U.S. Pat. No. 4,766,763 entitled GAS LEAK DETECTION APPARATUS AND METHODS issued to A. D. Kurtz on Aug. 30, 1988, and assigned to the same assignee as the present invention. That apparatus utilizes a pressure transducer, which produces an output voltage proportional to the gas pressure inside a containment vessel, and an amplifier circuit with a gain proportional to the reciprocal of the absolute temperature of the gas inside the vessel, to produce an output signal which indicates whether the vessel has a leak. The apparatus operates on the principle of the ideal gas law which states that, at normal temperatures and pressures, the pressure of a gas is given by the equation PV=nRT, where V is the volume occupied by the gas, P is the pressure of the gas, R is the universal gas constant, n is the number of moles of gas within the volume, and T is the absolute temperature of the gas. The output of the apparatus is proportional to the ratio of pressure to temperature, P/T, and, accordingly, is independent of temperature induced pressure changes. Therefore, for a fixed volume vessel, any change in the value of the output signal will be indicative of a change in the number of moles of gas contained in the vessel and thereby connote a leak. The apparatus uses a pressure transducer having a deflectable diaphragm operating in conjunction one or more pressure responsive resistors which typically will be disposed as part of a Wheatstone bridge array. An output signal from this transducer, which will be proportional to the pressure in the vessel, is then fed into an operational amplifier circuit which utilizes a temperature sensitive resistance to effect an overall circuit gain proportional to 1/T. The output of the combination of these two elements is therefore proportional to P/T.
While this device offers significant advantages over the leak detection devices that preceded it, there remains an inherent element of inaccuracy due to the fact that the ideal gas law is not a highly accurate model for the behavior of real gases. In general, real gases fail to behave in an ideal manner for two reasons. First, because all molecules are of finite dimensions, the presence of a molecule in a certain location in any given volume prevents another molecule from occupying the same space. This tends to make the volume occupied by the gas larger than that calculated using the ideal gas law. Second, there is always a slight attraction between the molecules of a gas, and this prevents the particles from moving independently of one another. This tends to make the volume occupied by the gas smaller than that calculated using the ideal gas law. While these opposing errors will tend to cancel one another, an exact cancellation seldom occurs. In general, gases with higher boiling points display larger deviations from ideal behavior, with the largest deviations occurring when the gas is approaching condensation.
Because of the deviation between the behavior of real gases and the behavior predicted by the ideal gas law, many equations have been developed which attempt to take into account the characteristics of each particular gas in predicting how that gas will behave. One of the most useful of these equations is the van der Waals equation: ##EQU1## where P is the pressure, V is the volume, R is the universal gas constant, T is the absolute temperature, n is the number of moles of gas, and a and b are constants which are characteristic of each gas. The constant "a" concerns the energy of attraction between the molecules of the gas and the constant "b" concerns the physical space taken up by the molecules of the gas. These constants are usually found by experiment. Once these constants are found, the van der Waals equation offers a much more accurate model of the behavior of real gases than does the ideal gas law.